Solitary Wave Solutions for the Boussinesq and Fisher Equations by the Modified Simple Equation Method
Md. Ashrafuzzaman Khan,
M. Ali Akbar,
Fethi Bin Muhammad Belgacem
Issue:
Volume 2, Issue 1, February 2016
Pages:
1-18
Received:
14 November 2015
Accepted:
30 March 2016
Published:
3 June 2016
DOI:
10.11648/j.ml.20160201.11
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Abstract: Although the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations in the field of engineering and mathematical physics, it has some drawbacks. Particularly, if the balance number is greater than 1, the method cannot be expected to yield any solution. In this article, we present a process to implement the modified simple equation method to solve nonlinear evolution equations for balance number greater than 1, namely with balance number equal to 2. To validate our theory through applications, two equations have been chosen to undergo the proposed process, the Boussinesq and the Fisher equations, to which traveling wave are found and analyzed. For special parameters values, solitary wave solutions are originated from the exact solutions. We analyze the solitary wave properties by the graphs of the solutions. This shows the validity, usefulness, and necessity of the process.
Abstract: Although the modified simple equation method effectively provides exact traveling wave solutions to nonlinear evolution equations in the field of engineering and mathematical physics, it has some drawbacks. Particularly, if the balance number is greater than 1, the method cannot be expected to yield any solution. In this article, we present a proce...
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